Is there a date when interview invitations stop going out? Some said that interview invitations will come between mid-Jan and mid-Feb, so can an applicant assume that by March or mid-March there will be no more interview invitations?
I don't think there is a single answer here. Some schools start their interview process in late fall, and other schools don't even conduct preliminary interviews until the end of February. In addition, there's always the possibility that nobody accepts their initial offers, in which case they may want to start a new round of interviews. So basically, you can get an interview request until you get a rejection letter.
However, I would suspect that the bulk of interview requests go out by late February.
It depends on the field you're in. I'm familiar with Math and there, all research schools probably finish hiring at the end of February. We might have sent offers in March, but I don't think we ever invited anyone after mid-February.
Of course, the timeline is completely different for senior hires where there is, essentially, no timeline at all. But I assume that's not what you were asking for.
As some folks have mentioned, it will depend greatly based on the field. My own field doesn't even have a well-defined cycle - there are job announcements posted essentially continuously, which means a similarly continuous trickle of possible interview invitations, and some announcements are held open a remarkably long time.
It may be useful to consult someone specifically in your field, such as your advisor, or another faculty member you trust.